# Topological drum theorem

M. Postnikov in his lections on geometry write that the theorem

Sphere $S^{n-1}$ isn't retract of ball $B^n$.

calls "Drum theorem" because for $n=2$ it mean that we can stretch a film over a circle and make drum.

But I don't understand. Why?

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Well, if the Disk would retract to the circle, the drum would not drum if you drum it. The material would flow smoothly to it's border – Blah Mar 16 '12 at 10:58
@Blah: Cool! Thanks! It's so simple... – Corvus Mar 16 '12 at 11:10

This fact, essentially the material of elementary geometry, which for $n=2$ is immediately obvious as the possibility to stretch drumhead on a hoop, still has no proof without the methods of algebraic topology.
этот, по существу, элементарно-геометрический и (при $n = 2$) наглядно очевидный факт (физически означающий возможность натянуть на круглый обруч барабан) до сих пор не удалось доказать без привлечения алгебраико-топологических методов.